Question

a number line with points l and m is shown. point l weighs \\( \frac { 2 } { 3 } \\). point m weighs \\( \frac { 1 } { 3 } \\). find the coordinate of point s that represents the weighted averages of points l and m. if the weight of point l is decreased to \\( \frac { 1 } { 3 } \\) and the weight of point m is increased to \\( \frac { 2 } { 3 } \\), the coordinate of s would decrease. the coordinate of point s is \\( - 2 \\). if the weight of point l is increased, the weighed average would increase. if the weight of point m is increased, the weighed average would increase.

Explanation:

Step1: Calculate the initial weighted average

The formula for weighted average \(S = w_1x_1+w_2x_2\), where \(w_1=\frac{2}{3},x_1 = - 10\), \(w_2=\frac{1}{3},x_2=2\)

$$
LATEXBLOCK0
$$

Step2: Analyze each option

• Option 1:

New \(w_1=\frac{1}{3},x_1=-10\), \(w_2=\frac{2}{3},x_2 = 2\)

$$
LATEXBLOCK1
$$

\(-2>-6\), so the coordinate of \(S\) would increase. This option is wrong.

• Option 2:

From Step1, the initial coordinate of \(S\) is \(-6
eq - 2\). This option is wrong.

• Option 3:

Since \(x_1=-10

• Option 4:

Since \(x_1=-100\)) will increase. This option is correct.

Answer:

If the weight of Point M is increased, the weighed average would increase.